Stability and performance analysis of networks supporting services with rate control-could the Internet be unstable?

Abstract

Abstract--We consider the stability and performance of a model for networks supporting services that adapt their transmission to the available bandwidth. Not unlike real networks, in our model, connection arrivals are stochastic, each has a random amount of data to send, and the number of ongoing connections in the system changes over time. Consequently, the bandwidth allocated to, or throughput achieved by, a given connection may change during its lifetime as feedback control mechanisms react to network loads. Ideally, if there were a fixed number of ongoing connections, such feedback mechanisms would reach an equilibrium bandwidth allocation typically characterized in terms of its "fairness" to users, e.g., max-min or proportionally fair. In this paper we prove the stability of such networks when the offered load on each link does not exceed its capacity. We use simulation to investigate performance, in terms of average connection delays, for various fairness criteria. Finally, we pose an architectural problem in TCP/IPs decoupling of the transport and network layer from the point of view of guaranteeing connection-level stability, which we claim may explain congestion phenomena on the Internet.Index Terms--ABR service, bandwidth allocation, Lyapunov functions, performance analysis, proportional fairness, rate control, stability, TCP/IP, weighted max-min fairness.

Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

“…This question is still not settled, in general, and it is not the subject matter of the present paper although a variety of results may be found in De Veciana et al (1999, Bonald and Massouliè (2001), Mo and Walrand (2000), Massoulié (2007), Gromoll and Williams (2008), and Chiang et al (2006). Another significant issue, which is more central to the present paper, is concerned with second order phenomena, i.e., methods to evaluate the performance of bandwidth-sharing models.…”

On multiplexing flows: Does it hurt or not?

“…Massoulié and Roberts showed that randomness in the number of parallel flows can have unpredictable consequences on the throughput of long-lived flows, irrespective of the assigned weights to the parallel flows [32]. In a similar setting, Bonald and Massoulié demonstrated that network stability is insensitive to a broad range of fair allocations [10], generalizing a result of de Veciana et al for weighted max-min fairness [43]. A more recent study of Liu et al showed that stability is actually sensitive to the settings of α-fairness, in networks with non-convex and time-varying rate regions [29], generalizing an earlier result of Bonald and Proutière [11].…”

A stability conjecture on bandwidth sharing networks

“…Subsequently, De Veciana and Konstantopoulos [12] prove that (1.1) is sufficient for the stability for both proportionally fair and max-min fair allocation policies under a general network topology. De Veciana and Konstantopoulos [12] proved the stability by the construction of an appropriate Lyapunov function and then by applying Foster's lemma.…”

“…De Veciana and Konstantopoulos [12] proved the stability by the construction of an appropriate Lyapunov function and then by applying Foster's lemma.…”